1. Standard GMM problem Consider the i.i.d. Normal stochastic process, {=} , with Ex, = and E(X, )2 = 02. Let 14 = E(14 u)' denote the Ith moment about the mean. A property of the Normal distribution is that odd-ordered moments are zero, and even- ordered moments satisfy: Mzk = 20. Skewness of any distribution is defined as EX, ) In the case of a Normal distribution, this is of course zero. Skewness is estimated as follows: , (- ) ST 92 [(*) mil?. ^ = } (a) Set this estimator of skewness up as an exactly identified GMM estimator. Find the asymptotic distribution of Sr. (b) Now suppose that the true value of the mean is known. Find the asymptotic distribution of Sr. (Hint: to do each part of this question, you have to identify a different "GMM stochastic process", hx(0,), having the property, Eh: (0, wx) = 0, where 0" is the true value of the parameters, and 0 = (44,0, s) in the case of part a, while 8 = (0, 3)' in the case a of part b. When computing the matrices required by GMM, be sure to impose all the properties of the Normal distribution.) 1. Standard GMM problem Consider the i.i.d. Normal stochastic process, {=} , with Ex, = and E(X, )2 = 02. Let 14 = E(14 u)' denote the Ith moment about the mean. A property of the Normal distribution is that odd-ordered moments are zero, and even- ordered moments satisfy: Mzk = 20. Skewness of any distribution is defined as EX, ) In the case of a Normal distribution, this is of course zero. Skewness is estimated as follows: , (- ) ST 92 [(*) mil?. ^ = } (a) Set this estimator of skewness up as an exactly identified GMM estimator. Find the asymptotic distribution of Sr. (b) Now suppose that the true value of the mean is known. Find the asymptotic distribution of Sr. (Hint: to do each part of this question, you have to identify a different "GMM stochastic process", hx(0,), having the property, Eh: (0, wx) = 0, where 0" is the true value of the parameters, and 0 = (44,0, s) in the case of part a, while 8 = (0, 3)' in the case a of part b. When computing the matrices required by GMM, be sure to impose all the properties of the Normal distribution.)